Syllabus for Graph Theory

Grafteori

Syllabus

  • 5 credits
  • Course code: 1MA170
  • Education cycle: First cycle
  • Main field(s) of study and in-depth level: Mathematics G1F

    Explanation of codes

    The code indicates the education cycle and in-depth level of the course in relation to other courses within the same main field of study according to the requirements for general degrees:

    First cycle
    G1N: has only upper-secondary level entry requirements
    G1F: has less than 60 credits in first-cycle course/s as entry requirements
    G1E: contains specially designed degree project for Higher Education Diploma
    G2F: has at least 60 credits in first-cycle course/s as entry requirements
    G2E: has at least 60 credits in first-cycle course/s as entry requirements, contains degree project for Bachelor of Arts/Bachelor of Science
    GXX: in-depth level of the course cannot be classified.

    Second cycle
    A1N: has only first-cycle course/s as entry requirements
    A1F: has second-cycle course/s as entry requirements
    A1E: contains degree project for Master of Arts/Master of Science (60 credits)
    A2E: contains degree project for Master of Arts/Master of Science (120 credits)
    AXX: in-depth level of the course cannot be classified.

  • Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
  • Established: 2010-03-18
  • Established by:
  • Revised: 2018-08-30
  • Revised by: The Faculty Board of Science and Technology
  • Applies from: week 30, 2019
  • Entry requirements: 35 credits in mathematics including Linear Algebra II and Probability and Statistics or Probability Theory I.
  • Responsible department: Department of Mathematics

Learning outcomes

On completion of the course, the student should be able to:

  • know some important classes of graph theoretic problems;
  • be able to formulate and prove central theorems about trees, matching, connectivity, colouring and planar graphs;
  • be able to describe and apply some basic algorithms for graphs;
  • be able to use graph theory as a modelling tool.

Content

Basic graph theoretical concepts: paths and cycles, connectivity, trees, spanning subgraphs, bipartite graphs, Hamiltonian and Euler cycles. Algorithms for shortest path and spanning trees. Matching theory. Planar graphs. Colouring. Flows in networks, the max-flow min-cut theorem. Random graphs. Structural properties of large graphs: degree distributions, clustering coefficients, preferential attachment, characteristic path length and small world networks. Applications in biology and social sciences.

Instruction

Lectures, lessons and problem solving sessions.

Assessment

Written examination at the end of the course combined with written assignments during the course according to instructions at course start.

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.

Reading list

Reading list

Applies from: week 30, 2019

Some titles may be available electronically through the University library.

  • Diestel, Reinhard. Graph theory

    4th ed.: Heidelberg: Springer, c2010.

    Find in the library

  • Föreläsarens material och anteckningar

    Matematiska institutionen,